How do you explain why an angle is 90 degrees?

Understanding the Concept of 90-Degree Angles

In geometry, an angle is formed by two intersecting lines or rays. The measure of an angle is expressed in degrees, with 90 degrees representing a right angle.

Perpendicular Lines and Right Angles

Two lines are said to be perpendicular if they intersect at a right angle. At their intersection point, they create four right angles, each measuring 90 degrees. This is because a right angle is half of a complete rotation, which measures 360 degrees.

Altitude and Right Angles

In a triangle, an altitude is a line segment that is drawn from a vertex perpendicular to the opposite side. The point where the altitude intersects the opposite side forms a right angle. This is because the altitude divides the opposite side into two equal parts, and the angle formed by the altitude and the opposite side is equal to the angle formed by the altitude and the other two sides of the triangle.

Properties of 90-Degree Angles

• Right angles are equal to each other.
• Two angles that are supplementary (adding up to 180 degrees) will each measure 90 degrees if one of them is a right angle.
• A triangle with two right angles is called a right triangle.
• The sum of the interior angles of a quadrilateral is 360 degrees. If a quadrilateral has four right angles, it is a rectangle or a square.

Applications of 90-Degree Angles

Right angles are commonly used in engineering, architecture, and design. They are essential for ensuring the stability and precision of structures and objects. For example:

• In building construction, right angles are used to create square corners and level floors.
• In furniture design, right angles are used to ensure that tables, chairs, and other pieces of furniture are stable and sturdy.
• In mechanical engineering, right angles are used in the design of gears, pulleys, and other rotating components.